A method of the kind described in the opening paragraph and a press for carrying out this method are known from the German Patent 838.438 which corresponds to U.S. Pat. No. 2,657,429. In a first phase of this known method, a first mold part is moved from an initial position parallel to a central axis to a second mold part by means of a liquid medium which is pumped into a cylinder under a first pressure (for example, 35 at), upon which in a second phase the same liquid medium is brought under a second, increased pressure (for example, 200 at) in order to press the mold parts together. After the solidifiable liquid placed in the mold has cured or solidified, the first mold part is returned to the initial position by purely hydraulic means. A disadvantage of the known method and press is that the quantity of hydraulic liquid medium which is displaced for opening and closing the mold parts is comparatively great, so that a comparatively large hydraulic pump is required with an associated cooling device for cooling the liquid medium. The total quantity of energy required for opening and closing the mold parts as a result is also comparatively great.